A woman at a point A on the hore of a circular lake with radiu 2 mi want to arrive at the point C diametrically oppoite A on the other ide of the lake in the hortet poible time (ee the figure). She can walk at the rate of 4 mi/h and row a boat at 2 mi/h. For what value of the angle hown in the figure will he minimize her travel time?

Average area of the cross section plane of the solid which lies between the two parallel planes is equal to 197.4square feet.

As given in the question,

Number of parallel planes = 2

Distance between two parallel planes = 22 feet

Volume of the solid is equal to 4343 cubic feet

Let 'x' be the average area of cross section of the solid lies between two parallel planes.

Average area of cross section of the solid lies between two parallel planes  = Volume of the solids / Distance between two parallel planes

⇒ x = 4343/22 square feet

⇒ x = 197.4 square feet

Therefore, the average area of the cross section of the solid lies between two parallel plane is equal to 197.4 square feet.

The complete question is:

A solid lies between two parallel planes 22 feet apart and has a volume of 4343 cubic feet. What is the average area of cross-sections of the solid by planes that lie between the given ones?

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Yes, the given expressions are equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

9(4 - x)

and 36 - 9x

Are these equivalent expressions?

9(4 - x) = 36 - 9x

36 - 9x = 36 - 9x

So, LHS = RHS = 36 - 9x

Therefore, the expression 9(4 - x) and 36 - 9x  are equivalent expressions.

Hence, yes the given expressions are equivalent.

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Answer:

[tex]\text{as x} \to \infty, \ \text{y} \to -\infty\\\\\text{as x} \to -\infty, \ \text{y} \to \infty[/tex]

Rises to the left; falls to the right

============================================================

Explanation:

The leading term is what determines the end behavior of any polynomial function.

The leading term has the largest exponent. The other terms will have no effect on the end behavior.

As x gets really large in the positive direction, so does x^3. But the -2 out front will flip to have y go to negative infinity.

Therefore:  [tex]\text{as x} \to \infty, \ \text{y} \to -\infty[/tex]

We can informally think of this as "falls to the right".

---------------------------

As x heads to the left, x^3 becomes further negative. But -2 out front makes -2x^3 to be positive.

So [tex]\text{as x} \to -\infty, \ \text{y} \to \infty[/tex] aka "rises to the left".

Whatever x does, y does the opposite. If x goes positive, then y goes negative and vice versa.

-------------------------

The end behavior is therefore

[tex]\text{as x} \to \infty, \ \text{y} \to -\infty\\\\\text{as x} \to -\infty, \ \text{y} \to \infty[/tex]

x and y are opposite.

We can summarize that notation as saying "rises to the left, falls to the right".

See the graph below. I used GeoGebra to make the graph, but you can use Desmos or any other tool you prefer.

18.75 inches is the length of the rectangle and 18.75 inches is the width of rectangle.

The area of Rectangle is length times of width.

The perimeter of a rectangle is 50 inches.

Perimeter=2(Length+Width)

Length=3W

Perimeter=50 inches

50=2(3W+W)

50=2(4W)

50=8W

Divide both sides by 8

50/8=W

W=6.25

Length=3(6.25)=18.75.

Hence, the length of rectangle is 18.75 inches and width is 6.25 inches.

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Answer:

It takes 38.5 years for money to quadruple when invested at an annual interest rate of 1.8% compounded continuously.

The solution to this problem is the p-value must be higher than 0.05.

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here ,

In this given problem we can see confidence interval has 0 in it.

So,

Since the confidence interval comprises 0, the null hypothesis should be rejected.

When the p-value exceeds the level of significance, the null hypothesis is only rejected.

Since alpha=0.05 in this case, the p-value must be higher than 0.05.

Thus, the p-value must be higher than 0.05.

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Answer:

3w + 2

Step-by-step explanation:

3(w + 1) - 1

(3 · w) + (3 · 1) - 1

3w + 3 - 1

3w + 2

Answer:

37.7

Step-by-step explanation:

Circumference = π × d = 3.14 × 12 = 37.68

Answer:

37.7

Step-by-step explanation:

circumference = πd

12(3.14) = 37.7 (nearest 1 d.p.)

The constant of proportionality representing the distance travelled by the runner is equivalent to 9.1.

The general equation of a straight line is -

The equation can also be used to represent direct proportionality as -

m is called constant of proportionality

Given is a table that shows the distance traveled by a runner.

We can write the constant of proportionality as -

m = (13.65 - 4.55)/(1.5 - 0.5)

m = 9.1

Therefore, the constant of proportionality for the data that shows the distance travelled by the runner will be 9.1.

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Twice a number is equal to negative four :

                       2n = -4

Equation:

An equation is a formula that expresses equality by connecting two expressions with an equal sign '='. Equations and their cousins ​​in other languages ​​may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, but in English any formula in its proper form consisting of two equations joined by an equal sign is an equation.

The equation resembles a weighted scale. When two bowls have the same weight (such as grain), the two weights balance the scale and are said to be equal. If you remove a certain amount of grain from one pan of the scale, you must remove the same amount of grain from the other pan to keep the scale balanced. More generally, the equation remains in equilibrium if the same operation is performed on both sides.

According to the question:

If you wanted to solve your equation:

   2x = -4

⇒ 2x/2 = -4/2

Divide both sides by 2

For getting the value of x only:

x = -2

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The amount of money the carnival committee should expect to pay for prizes for the booth is 218.7 dollars.

Therefore, the answer is option C.

At a booth at the school carnival in past years, they've found that 22% of students win a stuffed toy ($3.60), 16% of students win a jump rope ($1.20), and 6% of students win a t-shirt ($7.90). The remaining students do not win a prize.

If 150 students play the game at the booth, the amount of money the carnival committee expect to pay for the prizes of the booth is as follows:

total student that partake = 150

number that win stuffed toy  = 22% of 150

number that win stuffed toy = 33

number that win  jump rope = 16% of 150

number that win  jump rope = 24

number that win  t-shirt = 6% of 150

number that win  t-shirt = 9

Therefore,

prizes for those that win stuffed toy = 33 × 3.60 = 118.8 dollars

prizes for those that win jump rope = 24 × 1.20 = 28.8 dollars

prizes for those that win t-shirt = 9 × 7.90 = 71.1 dollars

Hence,

total amount the committee is expected to pay for prizes = 118.8 + 28.8 + 71.1 = 218.7 dollars

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Jasmine sold the fidget spinner to Bryan for the cost of $5.55.

To find the cost that Jasmine sold the fidget spinner to Bryan for, we need to first find the amount of the markup by multiplying the original price by the markup percentage.

As per the question, the original price of the fidget spinner is $3, and the markup percentage is 850%, so the markup amount is :

$3 × 850% = $2.55.

Next, we need to add the markup amount to the original price to find the selling price. So, the selling price is :

$3 + $2.55 = $5.55.

Therefore, Bryan paid $5.55 for the fidget spinner that Jasmine had just sold him.

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Answer:

w(3n)=12n+2

Step-by-step explanation:

. Explanation: to evaluate w(3n) substitute n=3n into w(n). ⇒w(3n)=4(3n)+2=12n+2.

Answer: 46%

Step-by-step explanation:

A polynomial function f is equal to x^3- 11x^2+41x- 51 of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

The degree of this polynomial is 3 and the leading coefficient is 1. Three zeros are 3, 4+i, 4-i bc, and a-bi if a+bi is zero, also known as the conjugate postulate. With this information, we can say that the factors are (x-3)(x-(4+i) )(x-(4-i)).

When we start multiplying, we group like this

(x-3)( (x-4) + i )( (x-4) -i )

Multiply the second two factors first.

(x-4)^2 - (i)^2 [This is the difference of squares (a+b)(a-b)].

We know that

i^2 = -1

= x^2 -4x -4x +16 - (-1)

= x^2-8x+16+1

= x^2 -8x +17

Don't forget (x-3).

Solving complete factors

(x-3)(x2-8x+17)

= x^3 -8x^2 +17x -3x^2 +24x -51

= x^3-11x^2+41x-51

This is the final equation of the polynomial.

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The steps to solve the 3 linear equations with 2 variables is shown below .

In the question ,

it is asked that how can we find the solution of 3 linear equations that have 2 variables .

Step (1) : Pick any two pair of linear equations ,

Step(2) : Then use addition and subtraction to eliminate the Same Variable from the equations .

Step(3) : In step 2 we will get the value of 1 variable ,

Step(4) : Substituting the value of the variable in Step(2) in the third linear equation ,

we will get the value of other variable also .

Therefore , the value of both the variable can be found by the above steps .

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Answer:

his gives us that Chris is walking 69 feet per minute faster than Heidi.

Step-by-step explanation:

1 mile is equal to 5,280 feet, we can multiply 3 by 5,280 to find that Heidi is walking 15,840 feet per hour.

Next, we need to convert both speeds to feet per minute. Since there are 60 minutes in an hour, we can divide both speeds by 60 to convert them to feet per minute. This gives us that Heidi is walking 264 feet per minute and Chris is walking 333 feet per minute.

Finally, to find out how much faster Chris is walking than Heidi, we can subtract Heidi's speed in feet per minute from Chris's speed in feet per minute.

Answer:

A. One Solution

Step-by-step explanation:

To determine if a system of equations has no solutions, infinitely many solutions, or exactly one solution, we can solve the system by any method, such as elimination or substitution.

In this case, we can solve the system by elimination. Multiplying the first equation by -2 and adding it to the second equation, we get:

0x + 4y = -3

This equation tells us that y must be equal to -3/4, but we still need to check if this value of y satisfies the original equations. Substituting -3/4 for y in the first equation, we get:

2x + (-3/4) = 7

Solving this equation for x, we get x = 5/4. Substituting this value of x and -3/4 for y in the second equation, we get:

-2(5/4) + 2(-3/4) = -5

which simplifies to:

-5/2 + (-3/2) = -5

This equation is true, so the solution of the system is x = 5/4 and y = -3/4. Since the system has a unique solution, the answer is (A) One Solution.

The amount of money each person get at the end of the summer is below;

You = $80

Kyra = $102

Paolo = $98

Total contribution = $22 + $18 + $0

= $40

Amount each person get = (Total earnings after investment - Total contribution) / 3

= ($280 - $40) / 3

= $240/3

= $80

Amount you get = Your contribution + Amount each person get

= 0 + 80

= $80

Amount Kyra get = Kyra contribution + Amount each person get

= $22 + $80

= $102

Amount Paolo get = Paolo contribution + Amount each person get

= $18 + $80

= $98

In conclusion, each person gets an equal amount including their invested money.

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Answer:

x = 28

Step-by-step explanation:

We can write a proportion to solve

50 dollars       175 dollars

--------------- = --------------------

8 hours                  x hours

Using cross products

50x = 8 * 175

Divide each side by 50

x = 8 * 175 / 50

x = 28

Answer:

[tex]\huge\boxed{\sf 28 \ hours}[/tex]

Step-by-step explanation:

Given that,

$50 = 8 hours

Divide both sides by 50

$1 = 8/50 hours

$1 = 0.16 hours

Multiply 175 to both sides

$175 = 0.16*175 hours

[tex]\rule[225]{225}{2}[/tex]

The expression after simplifying is 4b + 3r

What is Expression ?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

According to question

The total cost of the rice = 6b

The total cost of the bean = 4r

The total cost of the rice and bean Gabriel bought = 6b + 4r

The total cost after the return =  (6b 4r) – (2b + r)

Simplifying

⇒ (6b + 4r) – (2b + r)

⇒ (6b + 4r) – 2b - r

⇒ 6b + 4r – 2b - r

⇒ 6b – 2b + 4r - r

⇒ 4b + 3r

hence, The expression after simplifying is  4b + 3r

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We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this difference. A polynomial is divided by another polynomial in an arithmetic operation called division, usually with a lower degree than the dividend. A polynomial may or may not be produced when two polynomials are divided.

Take Dividend as (2x^3 + 5x^2 - x + 6)

Take Divisor denominator as (x-3)

By using long hand division technique,

    (2x^3+5x^2-x+6)/(x-3)

  ⇒(x-3)(2x^2+11x+32)/(x-3)

 ∴ The quotient for the given polynomial division is 2x^2+11x+32 and the    

   Remainder for the polynomial division is 90.

We can use polynomial division concept for the given question. The quotient for the polynomial division is (2x^2+11x+32).

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To horizontally translate a function,

1)substitute 'x-h' for 'x' in the function.

2)The value for 'h' controls how much the graph shifts to the left or right

3)In our example, since h = -4, the graph shifts 4 units to the left

4)To vertically translate a function, add 'k' onto the end

5)The value for 'k' controls how much the graph shifts up or down

You can also perform both horizontal and vertical translations on a function at the same time!

Translation

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input.

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The other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.

A polynomial is an expression of one or more algebraic terms, each of which is composed of constants and/or variables raised to non-negative integer powers. A polynomial can be written in the form of an equation, where the coefficients of the terms form a sequence of numbers. Polynomials can also be expressed using a factored form, in which each of the terms is the product of a coefficient and a single variable or factor. Polynomials are commonly used to model real-world phenomena, such as the behavior of a system or process. The degree of a polynomial, which is the highest degree of the terms, determines the number of solutions it has. For example, a polynomial of degree two has two solutions while a polynomial of degree three has three solutions. The solutions of a polynomial are determined by solving the equation formed by the polynomial's terms.

Let us first rewrite the polynomial in a standard form:

2x^3 + 7x^2 + ax + 2 = 0
We can factor this polynomial using the Factor Theorem. The Factor Theorem states that if a is a root of a polynomial, then x-a is a factor of the polynomial.
Since x=-2 is a root of the polynomial, the factor (x+2) must be a factor of the polynomial.
Therefore, we can rewrite the polynomial as:
2x^3 + 7x^2 + ax + 2 = 2(x+2)(x^2 + bx + c)
Now, we can use the coefficients of the polynomial to solve for a, b and c.
Comparing the coefficients of the polynomial on both sides:
2 = 2c
7 = b
a = -2b-4c
Substituting the values of c and b in the equation for a, we get:
a = -2(b) - 4(2)
 = -2(7) - 8
 = -16
Therefore, the value of a is -16.
To find the other roots of the polynomial, we just need to solve the remaining factor (x^2 + bx + c) = 0.
Substituting the values of b and c, we get:
x^2 + 7x + 2 = 0
We can solve this equation using the Quadratic Formula:
x = [-b ± √(b^2 - 4ac)]/2a

Substituting the values of a, b and c, we get:
x = [-7 ± √(7^2 - 4(2)(2))]/2(-2)
 = [-7 ± √(49 - 16)]/-4
 = [-7 ± √33]/-4
Therefore, the other two roots of the polynomial are x = (7 + √33)/4 and x = (7 - √33)/4.

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The student react that to ask for a cost-of-living increase to her stipend when a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.

Given that,

In the United States, a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.

We have to find how may the pupil respond.

We know that,

The term "inflation" describes an increase in the cost of any goods or services.

A history graduate who was living in the United States at the time was given an allowance of $18,000. However, the United States economy is negatively impacted by significant inflation. As a result, the price of goods and services that are available to the public rises quickly. Nowadays, everyone has to spend more on everything. As a result, the graduate student must request that the cost of living be added to the stipend because they must now spend more on living expenses.

Therefore, The student react that to ask for a cost-of-living increase to her stipend when a graduate student studying economics receives an annual stipend of $18,000. U.S. inflation is quite high.

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The steps to solve a word problem are to read, plan and solve the problem.

1. Read: After reading the issue, decide what the question is trying to get to.

Read the issue at least twice.

Highlight or highlight important words, phrases, and numbers. Put an end to unimportant information.

2. Plan: Consider what the narrative is requesting of you. What facts are provided to you, and what do you need to learn?

Make a drawing.

Keywords may be underlined or circled. (Use crayons or highlighters to color-code important numbers and words.)

Put your own words in the question's place.

3. Solve: Which approach—addition, subtraction, multiplication, or division—could you use to uncover the information that is missing?

Create and solve a numerical sentence.

Employ counters.

Produce charts

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After solving we can conclude that (c) f(x) = -x is an odd function.

If -f(x) = f(-x), then a function f is said to be odd for all values of x.

When taking into account additive inverses, the functions even and odd are those that satisfy particular symmetry relations.

They are crucial to understanding power, the Fourier series, and mathematical analysis.

So, (a) f(x) = x³ + 5x² + x:

f(-x) = (-x)³ + 5(-x)² + (-x)

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

Neither even nor odd describe the function.

(b) f(x) = x² + x

f(-x) = (-x)² + (-x)

       = -(-x² + x)

Neither even nor odd describe the function.

(c) f(x) = -x

f(-x) = -(-x)

      = x

      = -f(x)

f(-x) = -f(x) makes the function odd.

Therefore, after solving we can conclude that (c) f(x) = -x is an odd function.

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Complete question:
Which of the following is an odd function?

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

The missing terms will be 0.5, 2, and 7.5 respectibily.

What is equivalent ratio?

The concept of a ratio in mathematics is the divisional comparison of two quantities, the antecedent and consequent. As an illustration, each ingredient must be added according to a ratio during cooking. So, we may argue that a ratio is employed to represent one quantity as a portion of another. The ratio can be written as a fraction as well. If the ratio a:b is a fraction, its form is a/b. As a result, it is simple to compare two or more equivalent ratios expressed as equivalent fractions.

1st ratio is 8:16 = 1/2

So the following terms will be 1:0.5

For 4 it will be 4:2.

For15 it will be 15:7.5.

Hence, The missing terms will be 0.5, 2, and 7.5 respectibily.

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Answer:

All sum of Traingle Angle is 180°

180= 87+31+ Angle C

Angle C = 180 - (31+87)

Angle C = 62